Consider the titration of the weak acid HA with NaOH. At what fraction of Ve does pH = pKa - 1? At what fraction of Ve does pH = pKa + 1? Calculate the pH at these two points plus Vb = 0, 1/2Ve, Ve and 1.2Ve, if 100 mL of 0.100 M anilinium bromide (pKa = 4.601) is titrated with 0.100 M NaOH.
What's Ve, Vb etc?
Ve is volume at equivalence point
Vb is volume of base
To determine the fraction of Ve (equivalent volume) at which pH = pKa - 1 and pH = pKa + 1, we need to find the pH values at different points during the titration. Here's how you can calculate the pH at each of the specified volumes:
Step 1: Calculate the number of moles of HA initially present:
Given that 100 mL of 0.100 M anilinium bromide (HA) is titrated, we can calculate the moles of HA initially present using the formula:
moles of HA = initial volume (Liters) × concentration (Molarity)
moles of HA = (100 mL ÷ 1000 mL/L) × (0.100 M)
moles of HA = 0.010 moles
Step 2: Determine the number of moles of NaOH required for neutralization:
Since HA is a monoprotic acid, it requires one mole of NaOH to neutralize it. Therefore, the moles of NaOH required is equal to the moles of HA present initially.
Step 3: Determine the total volume at each specified point:
Using the volume of NaOH added during the titration, we can determine the total volume at each specified point by summing the initial volume of HA and the volume of NaOH added thus far.
Step 4: Calculate the moles of unreacted HA at each specified point:
The moles of unreacted HA can be calculated by subtracting the moles of NaOH (which have reacted with HA) from the initial moles of HA.
Step 5: Calculate the fraction of Ve at each specified point:
The fraction of Ve can be calculated using the formula:
fraction of Ve = (volume of NaOH added)/(total volume)
Step 6: Calculate the pH at each specified point:
To calculate the pH, we use the Henderson-Hasselbalch equation:
pH = pKa + log ([A-]/[HA])
Now, let's calculate the pH at each specified point:
1. Vb = 0 (initial conditions):
After calculating the moles of unreacted HA, we can substitute these values into the Henderson-Hasselbalch equation, where [A-] is the concentration of the conjugate base, and [HA] is the concentration of the acid (unreacted HA).
2. 1/2Ve:
To find the moles of unreacted HA at 1/2Ve, we need to determine the number of moles of NaOH added at this point. Since the total volume at 1/2Ve is half of Ve, we multiply the moles of NaOH required for neutralization by 1/2 to find the moles of NaOH added. We can then calculate the moles of unreacted HA at this point and substitute the values into the Henderson-Hasselbalch equation.
3. Ve:
At Ve, all the moles of HA have been neutralized. Therefore, the moles of unreacted HA are zero, and the pH can be calculated using the formula pH = pKa + log ([A-]/[HA]). The concentration of [A-] at Ve is equal to the concentration of the anilinium bromide initially added.
4. 1.2Ve:
Using a similar approach as in step 2, we calculate the moles of unreacted HA at 1.2Ve, substitute the values into the Henderson-Hasselbalch equation, and calculate the pH.
By following these steps, you can calculate the pH at each specified volume during the titration.